A criterion for a small change in the direction of the solutions of a linear system of differential equations as the result of small disturbances in the coefficients of the system

It is shown that of the systems $\dot x=A(t)x$, only systems with integral separability have the following property: when $\sup\limits_t\|B(t)-A(t)\|$ is small, to each solution $y(t)$ of the system $\dot y=B(t)y$, one may associatea solution $x(t)$ of the system $\dot x=A(t)x$, such that the angle between the vectors $x(t)$, $y(t)$ is small for all $t$.